A Random Forest Guided Tour

Tree Prediction

Each tree estimates the response at point \(x\) as:

\[ m_n(x; \Theta_j, D_n) = \sum_{i \in D_n(\Theta_j)} \frac{\mathbf{1}_{X_i \in A_n(x; \Theta_j, D_n)} Y_i}{N_n(x; \Theta_j, D_n)} \]

Random Forest Classification

Splitting Criteria:

• The Gini impurity measure is used to determine the best split:

\[ G = 1 - \sum_{k=1}^{K} p_k^2 \]

Prediction:

• Each tree makes a prediction using the majority class in the cell containing \(x\).
• Classification uses a majority vote:

\[ m_{M, n}(x; \Theta_1, \ldots, \Theta_M, D_n) = \begin{cases} 1 & \text{if } \frac{1}{M} \sum_{j=1}^{M} m_n(x; \Theta_j, D_n) > \frac{1}{2} \\ 0 & \text{otherwise} \end{cases} \]

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The Data

1. Where the data came from – FL based food packaging company

2. Size of data – 33,818 records, 17 variables

3. Key variables - Demographic, Behavioral, Seasonal

4. Preprocessing needed -

   1. TotalPrice – negative values
   2. Quantity – highly skewed
   3. Substrate – missing values

Data Schema

SSI Sales Data

Sales over Time

Analysis - Stutti

Analysis - Matt

Goal:

Predict whether an OPCO (distributor) falls within the top 25% of revenue using the quantity ordered, product, and substrate to try and identify key distribution channels where the company could focus marketing and advertising dollars.

Confusion Matrix

• 0: Non-high-revenue OPCO
• 1: High-revenue OPCO

Model Statistics

ROC Curve Analysis

Figure 1: ROC Curve for High Revenue Prediction

Feature Importance

Figure 2: Feature Importance for High Revenue Prediction

Analysis - Mika

Conclusion

• High Performance & Versatile: Robust, accurate, handles noisy/high-dimensional data. [1]
• Ensemble Strength: Averaging over many trees; identifies key variables. [1]
• Challenges: Limited theoretical understanding; complex interpretation. [1]
• Future Focus: Enhance theory, increase interpretability, broaden applications. [1]